Machine Learning
K‑Means Clustering of Interpolative
Separable Density Fitting Algorithm for Accurate and Efficient Cubic-Scaling
Exact Exchange Plus Random Phase Approximation within Plane Waves
posted on 2024-02-16, 07:30authored byZhenlin Zhang, Xilin Yin, Wei Hu, Jinlong Yang
The
exact-exchange plus random-phase approximation (EXX+RPA)
method
has emerged as a crucial tool for precisely characterizing electronic
structures in molecular and solid systems. We present an accurate
and efficient implementation of EXX+RPA calculations that scale cubically
and are conducted within plane waves. Our approach incorporates the
interpolative separable density fitting (ISDF) algorithm, effectively
mitigating the computational challenges associated with the plane
wave basis set. To overcome the constraints of the conventional ISDF
algorithm, characterized by the exceptionally high prefactor in QR
factorization for interpolation point selection, we introduce an enhanced
machine learning K-means method. This method incorporates a novel
empirical weight function called “SSM+” for more precise
interpolation point selection, capturing physical information more
accurately across diverse systems. Our machine learning approach offers
a quasiquadratic scaling alternative, effectively replacing the computationally
demanding cubic-scaling QRCP algorithm in plane-wave-based EXX+RPA
calculations. Furthermore, we enhance the method’s capabilities
by optimizing GPU acceleration using MATLAB’s integrated GPU
toolkit. In particular, our approach reduces the computational scaling
of χ0 from 3.80 to 2.13 and the overall computational
scaling of EXX from 2.74 to 2.10. We achieve a remarkable GPU acceleration
speedup of up to 35×. Regarding CPU computation time, the standard
quartic-scaling method requires 22 h to compute Si128,
while QRCP completes the calculation in only around 1 h, achieving
a speedup up to 20×. However, the utilization of the K-means
algorithm reduces the time to 800 s, a substantial improvement of
100× compared to the standard algorithm. By employing the K-means
algorithm, the computational time for interpolative point calculation
using QRCP decreases from 1 h to 1 min, resulting in a 55× speed
increase. With this improved algorithm, we successfully computed the
dissociation curve of H2 and the equilibrium polyynic geometry
of C18 molecules.